The hardware and hardware-cache events are a generic architecture independent abstraction of the PMU events. gator shows you the actual events supported by the PMU. You can see the mapping that perf makes here.

The software events can also be collected by gator but only in a recent version 6.7+ (DS-5.29) if I'm not mistaken.

So in summary, yes gator can collect all of the hardware, software and hardware-cache event plus others, they will just have specific names when using gator not the generic ones seen in perf list.